Suppose I have 3 vectors with length a,b,and c. They are oriented in 3D space such that the angles between the three vectors are $\alpha$, $\beta$, and $\gamma$ (suppose all less than 90 degrees).
If I set the vectors with length a and b on the x-y plane with angel $\alpha$ between them (set the vector with length a to be along x-axis), I am able to find the coordinates of the first two vectors. But then I run into trouble when I try to find the coordinates of the third vector based on its length c, and it's angles with the other two vectors $\beta$, and $\gamma$.
Can someone help me out? Thank you.